77/76: Difference between revisions

Interval information
Ratio	77/76
Factorization	2-2 × 7 × 11 × 19-1
Monzo	[-2 0 0 1 1 0 0 -1⟩
Size in cents	22.63083¢
Name	small undevicesimal 1/9-tone
Color name	19u1oz1, nulozo 1sn, ; Nulozo comma
FJS name	[math]\displaystyle{ \text{P1}^{7,11}_{19} }[/math]
Special properties	superparticular,; reduced
Tenney norm (log2 nd)	12.5147
Weil norm (log2 max(n, d))	12.5336
Wilson norm (sopfr(nd))	41
Comma size	small
	Open this interval in xen-calc

Latest revision as of 04:05, 27 May 2026

77/76 is a superparticular interval of about 22.6¢ which makes the difference between 8/7 and 22/19 in 19-limit just intonation; it is also the difference between 11/8 and 19/14.

The adjacent superparticulars 76/75 and 78/77 are also within the 19-limit, and 77/76 differs from them by 5776/5775 and 5929/5928 respectively.

It is close to one step of 53edo, and the comma associating it with 1\53 is tempered out in notable high-prime-limit systems like 159edo and 742edo.

@@ Line 6: / Line 6: @@
 '''77/76''' is a [[superparticular]] interval of about 22.6¢ which makes the difference between [[8/7]] and [[22/19]] in [[19-limit]] [[just intonation]]; it is also the difference between [[11/8]] and [[19/14]].
+The adjacent superparticulars [[76/75]] and [[78/77]] are also within the 19-limit, and 77/76 differs from them by [[5776/5775]] and [[5929/5928]] respectively.
 == Temperaments ==